This invention relates generally to sensor response linearization systems and methods, and more particularly to sensor response linearization systems and methods in a mass flow controller.
Transducers (sensors) are objects that convert one form of energy into another. There are many types of sensors, such as pressure sensors, electrical sensors, chemical sensors, and temperature sensors. Sensors provide information about the state of a process. This information is often used to both monitor and control the process. Sensors are widely used throughout the Semiconductor Industry to closely monitor and control various industry processes. As channel lengths and line widths decrease, allowable process variations in the Semiconductor Industry also decrease. Therefore, sensors in the Semiconductor Industry must produce accurate and reliable results so that processes can be carefully and precisely monitored.
One type of sensor often used in semiconductor processes is a flow sensor. A flow sensor measures the gas flow into a process chamber. Flow sensors are typically thermal sensors. A thermal flow sensor is often composed of two resistance temperature sensors wound around a capillary tube. When gas flows through the sensor, heat is carried downstream and the temperature difference is proportional to the mass flow rate of the gas. Unfortunately, many sensors, including flow sensors, have an innate non-linear response. Consequently, many methods have been implemented to linearize the output of the sensor prior to inputting the sensor signal into a control system.
Analog methods prior art sensor linearization has been achieved with non-linear electronic components such as diodes and transistors. These non-linear electronic components are often arranged in a compensating circuit topology such that the non-linear characteristic of the compensating circuit is the inverse of the sensors non-linear response. FIG. 1 illustrates the relationship between a correction response 10 of a compensating circuit topology, a sensor response 12, and the resulting linearized response 14.
Unfortunately, the use of compensating circuits has inherent problems. First, these types of compensating circuits are often adjusted manually by a technician and may be a tedious and time-consuming calibration process. Second, the non-linear components may change their characteristics with temperature and any shift of the null point may result in large errors in the corrected output. A null point shift also may be caused by the sensor itself. These sources of error can be reduced or completely eliminated by the digital methods.
Digital Methods include interfacing a sensor with a digital microprocessor. When the sensor is interfaced with a microprocessor, the non-linear sensor characteristics can be corrected by computational methods. These computational methods include polynomial curve fitting.
Unfortunately, digital methods also have some disadvantages. The coefficients of the polynomial curve are often calculated using mathematical formulas that may be too cumbersome for most microprocessors using integer arithmetic. Also, the calculations may include numbers that may be either too large or too small for the limited number field of the microprocessor for linearization. The situation is further aggravated if the degree of the polynomial is greater than two.
Other methods for sensor linearization include combining analog and digital techniques. These methods, however, also suffer from limitation caused by either additional circuit components or a limited number field in the microprocessor.
Ultimately there is a need for a technique for sensor response linearization that overcomes the disadvantages of prior art analog and digital methods of linearization. The method should enable calibration of a sensor with little or no manual interaction by a technician or engineer. Also the method should not be limited by the circuit or computer components assisting in the linearization process.
The present invention provides a system and method for sensor response linearization that substantially eliminates or reduces disadvantages and problems associated with previously developed systems and methods for sensor response linearization.
More specifically the present invention provides a method for generating a linearized sensor signal p from a sensor signal m using a kth-degree polynomial. The coefficients of the kth-degree polynomial can be calculated by using the least-squares method. The computer can calculate for 2 less than jxe2x89xa6k the (2jxe2x88x921) root of the jth coefficient aj of the kth-degree polynomial and download the coefficients and resulting roots rj to a storage device in a digital signal processor (DSP).
For 2 less than jxe2x89xa6k, the DSP can calculate       (                  a        j                  1                                    2              ⁢              j                        -            1                              ⁢      m        )    j
and multiply the result by             (              a        j                  1                                    2              ⁢              j                        -            1                              )              j      -      1        .
The resulting terms can be added to the calculation of a1m to generate the kth-degree polynomial. The kth-degree polynomial is the linearized sensor signal.
The present invention provides a technical advantage in that it does not require manual calibration or xe2x80x9ctweakingxe2x80x9d by a technician or engineer. Calibration is performed by a computer based on output of the sensor for various known process rates. The method does not require xe2x80x9ctweakingxe2x80x9d of analog circuit components to adjust compensating circuitry as with prior art analog methods of calibration.
The present invention also provides another technical advantage in that it can accommodate computer multiplication of very small and very large numbers. Calculations using such numbers may result in errors due to the limited number field on available microprocessors often used for control systems. By enabling accurate calculations with both very small numbers and very large numbers, the present invention provides a more accurate digital method of linearization.